Abstract

Road network analysis can require distance from points that are not on the network
themselves. We study the algorithmic problem of connecting a point inside a face
(region) of the road network to its boundary while minimizing the detour factor of that
point to any point on the boundary of the face. We show that the optimal single connection
(feed-link) can be computed in O(λ7(n) log n) time, where n is the number of vertices that
bounds the face and λ7(n) is the slightly superlinear maximum length of a Davenport-
Schinzel sequence of order 7 on n symbols. We also present approximation results for
placing more feed-links, deal with the case that there are obstacles in the face of the road
network that contains the point to be connected, and present various related results.